In this section we give an instantiation of the sparse recovery tool we use (Definition REF ) in Algorithms  - . Although the running times of our data structure are slightly worse (by some log factors) than the result of [1]}, it's enough for our symmetric norm estimation task. In terms of space requirement, the classical sparse recovery/compressed sensing only sublinear space is allowed. In our application, we're allowed to use linear space (e.g. \(d\)  per point, \(nd\)  in total). And more importantly, our instantiation has much simpler algorithm and analysis than the prior result.
